rum
around
Colloquial short form of 'herum' (around); expresses movement around something or in a circle.
Wir sind eine Stunde im Park rumgelaufen.
We walked around in the park for an hour.

around / over
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around
Colloquial short form of 'herum' (around); expresses movement around something or in a circle.
Wir sind eine Stunde im Park rumgelaufen.
We walked around in the park for an hour.

'Rum' is the colloquial short form of 'herum' (around). It is used almost exclusively in spoken language or in informal texts.
Lass uns noch eine Runde im Park rumgehen.
Let's walk around the park for another loop.
'Rum' is very often used as a separable part of verbs to describe an aimless, undefined, or repeated action. Examples include 'rumlaufen' (to walk/run around), 'rumsitzen' (to sit around), or 'rumliegen' (to lie around).
Die Kinder laufen den ganzen Tag im Garten rum.
The children run around in the garden all day.
In the meaning of 'vorbei' (over/past) or 'zu Ende' (finished), 'rum' is almost always used with units of time. Typical phrases are 'das Wochenende ist rum' (the weekend is over) or 'die Ferien sind rum' (the holidays are over).
Kaum hat der Urlaub angefangen, schon ist er wieder rum.
No sooner has the vacation started than it's already over again.
When 'rum' means 'ungefähr' (approximately), it usually comes after the time or quantity. It is often combined with words like 'so' (about) or 'gegen' (around).
Wir treffen uns so um sieben rum.
We'll meet at around seven.
In combinations like 'rumstehen' (to stand around) or 'rumliegen' (to lie around), 'rum' often has a slightly negative meaning. It implies that someone or something is useless or in the way.
Lass deine schmutzigen Socken nicht überall rumliegen!
Don't leave your dirty socks lying around everywhere!
about / approximately
'etwa' and 'rum' can both give an approximate figure or time. 'etwa' is neutral and fits everyday language, school, work, and written texts. 'rum' is colloquial and sounds especially natural with time expressions like 'um acht rum' (around eight o'clock) or with rough quantities. Learners may confuse the words because both can mean 'not exact'. But 'rum' also has other colloquial meanings, for example 'herum' (around) or 'vorbei' (over). For clear or more formal sentences, 'etwa' is safer.

Ich komme heute so um sieben rum vorbei.
I'll come by today at around seven.
Die Fahrt zum Bahnhof dauert etwa zwanzig Minuten.
The trip to the train station takes about twenty minutes.